freeware for linux

As far as finding application programs is concerned, all modern Linux distributions come with a package manager which can be used to find and install a required software package easily. All you have to do is search for the program you need, mark it for installation, and click "Apply" or something similar. And since almost all of the packages are free and open source, therefore you do not have to worry about cost and license in most cases.
I suggest that you start your journey with Ubuntu Linux because I think it will be easier for you than many others. However, it totally depends upon your own preferences which Linux distribution you choose.

The answer to your second question is that Linux and Windows are two different operating systems so applications designed for Windows will not run natively on Linux. But you can use "WINE" Windows emulator to run them on Linux. Notice that not all the Windows applications might run through WINE.

The answer to the third question is that Linux supports dozens of file-systems which also include FAT and NTFS. So you can access your Windows partitions from Linux. And most Linux distributions available nowadays make it as easy as possible to access those partitions. If you want advanced information then searching Google will be a nice idea.
The bad news is that you cannot access Linux partition from Windows without installing additional software. But I consider it as an advantage because it protects the files on the Linux partition from being corrupted by a virus. ;)

http://en.wikipedia.org/wiki/Wubi_(Ubuntu)